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Opuntia in Mexico: Identifying Priority Areas forConserving Biodiversity in a Multi-Use LandscapePatricia Illoldi-Rangel1*, Michael Ciarleglio1, Leia Sheinvar2, Miguel Linaje3, Victor Sanchez-Cordero3,

Sahotra Sarkar1,4

1 Biodiversity and Biocultural Conservation Laboratory, Section of Integrative Biology, University of Texas, Austin, Texas, United States of America, 2 Jardın Botanico

Exterior, Instituto de Biologıa, Universidad Nacional Autonoma de Mexico, Coyoacan, Mexico D.F., 3 Laboratorio de Sistemas de Informacion Geografica, Departamento de

Zoologıa, Instituto de Biologıa, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Coyoacan, Mexico D.F., 4 Department of Philosophy, University of Texas,

Austin, Texas, United States of America

Abstract

Background: Mexico is one of the world’s centers of species diversity (richness) for Opuntia cacti. Yet, in spite of theireconomic and ecological importance, Opuntia species remain poorly studied and protected in Mexico. Many of the speciesare sparsely but widely distributed across the landscape and are subject to a variety of human uses, so devisingimplementable conservation plans for them presents formidable difficulties. Multi–criteria analysis can be used to design aspatially coherent conservation area network while permitting sustainable human usage.

Methods and Findings: Species distribution models were created for 60 Opuntia species using MaxEnt. Targets ofrepresentation within conservation area networks were assigned at 100% for the geographically rarest species and 10% forthe most common ones. Three different conservation plans were developed to represent the species within these networksusing total area, shape, and connectivity as relevant criteria. Multi–criteria analysis and a metaheuristic adaptive tabu searchalgorithm were used to search for optimal solutions. The plans were built on the existing protected areas of Mexico andprioritized additional areas for management for the persistence of Opuntia species. All plans required around one–third ofMexico’s total area to be prioritized for attention for Opuntia conservation, underscoring the implausibility of Opuntiaconservation through traditional land reservation. Tabu search turned out to be both computationally tractable and easilyimplementable for search problems of this kind.

Conclusions: Opuntia conservation in Mexico require the management of large areas of land for multiple uses. The multi-criteria analyses identified priority areas and organized them in large contiguous blocks that can be effectively managed. Ahigh level of connectivity was established among the prioritized areas resulting in the enhancement of possible modes ofplant dispersal as well as only a small number of blocks that would be recommended for conservation management.

Citation: Illoldi-Rangel P, Ciarleglio M, Sheinvar L, Linaje M, Sanchez-Cordero V, et al. (2012) Opuntia in Mexico: Identifying Priority Areas for ConservingBiodiversity in a Multi-Use Landscape. PLoS ONE 7(5): e36650. doi:10.1371/journal.pone.0036650

Editor: Brock Fenton, University of Western Ontario, Canada

Received May 28, 2011; Accepted April 11, 2012; Published May 14, 2012

Copyright: � 2012 Illoldi-Rangel et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: Database development was supported by a project of the (Mexican) Comision Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO,Project No.GE005). PIR was supported by a post–doctoral grant from CONACyT (Project No. 51562/25048). The funders had no role in study design, data collectionand analysis, decision to publish, or preparation of the manuscript.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: [email protected]

Introduction

Traditional systematic conservation planning for biodiversity

consists of selecting priority areas to be designated as strictly

protected areas such as national parks or, more recently, as

reserves that permit some human; nevertheless, a conceptual

difference exists between areas that are protected and those that

are not [1–3]. However, if the biota of interest (the biodiversity

‘‘surrogates’’ sensu Sarkar and Margules [4]) is dispersed at low

densities over extended landscapes (for instance, on a continental

scale) that provide livelihoods for human populations, designating

such protected areas is typically neither feasible nor appropriate.

The maintenance of viable populations of all species would require

far too large an area that would have to be set aside from

continued human use. At the pragmatic level, any such policy is

likely to fail because successful conservation requires local support,

which would possibly not be forthcoming if livelihoods were

threatened [5,6]. More importantly, any policy that seriously

threatens (human) livelihoods only in the interest of preserving

biota is not ethically defensible [5,7,8]. This problem is further

intensified, especially in societies with economically disadvantaged

communities, when the biota to be protected themselves also have

everyday tangible human use, for instance, as food or construction

materials. It is imperative in such situations to find alternative

management strategies for conservation that go beyond the

protected areas model.

What is required in such circumstances is a reconceptualization

of priority areas so that they are not necessarily thought of as areas

qualitatively different from those that are in everyday human use

in the surrounding landscape matrix. These priority areas are still

conservation areas (sensu Sarkar [9]) but conservation means that

management is designed to foster the persistence of biodiversity

PLoS ONE | www.plosone.org 1 May 2012 | Volume 7 | Issue 5 | e36650

components: there is no endorsement, explicit or implicit, that the

management mode requires human exclusion and is thus akin to

the traditional national park model. This situation requires that

traditional conservation area selection methods [10] be modified

to take into account a variety of factors beyond the traditional

ecological ones of ensuring the adequate representation and

persistence of biodiversity [1]. The problem presents both

constraints and opportunities. With respect to the spatial

organization of priority areas, the constraints can be operationa-

lized as three criteria ideally to be satisfied: (i) areas should be

compact for ease of management; (ii) they should be connected, so

that there are as few distinct management units as possible; and (iii)

preferably, the areas should be aligned to a well-defined ecosystem

(habitat) type, or to existing protected areas, or to politically

homogeneous spatial units, so that a single management strategy

(or a small number of them) is adequate. (Some of these constraints

are also desirable in many circumstances to encourage the

persistence of species, for instance, dispersal [2,10] but that issue

will remain in the background in this paper). The major

opportunity is that the size (area) of the network of priority areas

need not be the absolute minimum to represent the biodiversity

surrogates. Since the goal is to foster the persistence of the

biodiversity while allowing human use, there can be tradeoffs

between spatial coherence and area minimization. If conservation

areas are to remain in human use, larger areas can be designated

for conservation than if they were to be precluded from such use.

Socio-economic criteria can be incorporated into algorithms for

the prioritization of individual conservation areas. Alternatively,

sets of conservation area networks may be algorithmically identify

on the basis of biodiversity representation and management

concerns, as discussed earlier, and further socio-economic

considerations then used to select one of these sets. The distinction

here is between iterative and terminal stage selection, respectively,

of conservation area networks [5,11]: in iterative protocols, all

socio-economic criteria are incorporated into algorithms as each

area is included in a set of nominal conservation areas; in terminal

stage protocols, entire sets of conservation areas are also assayed

for their performance under the socio-economic criteria. For both

protocols, multi-criteria analysis (MCA) must be used to incorpo-

rate the various biological, spatial, and socio-economic factors

[10]. If the study region (that is, the region for which the analysis is

being performed) is large, and the resolution used is fine (in this

case 0.02u), then precise socio-economic data are typically not

available for each potential habitat unit; this is the case for the

study area considered here. In such contexts, an iterative selection

of conservation areas incorporating all criteria is not possible and a

terminal stage protocol must be used.

Within the context of a terminal stage protocol for Opuntia

conservation throughout Mexico, this analysis prioritizes sets of

areas (nominal conservation area networks) that satisfy the

biodiversity representation and spatial management criteria using

a comprehensive data set assembled over the last 20 years. This is

done at a resolution that is fine enough for policy formulation at

the local level of municipalities, which are the most relevant

entities in Mexico for devising policies for the persistence of these

species while maintaining their human use. The size of the data set

presents formidable computational problems. If issues of spatial

coherence (compactness, connectivity, etc.) are ignored, the formal

(mathematical and computational) problem of selecting conserva-

tion areas is well–studied [10,12,13], and even large problems can

now be solved using optimal algorithms, that is, those that provide

an exact solution to the optimization problem. However, optimal

algorithms have yet to be devised to solve complex spatial

problems in reasonable times [10]. Heuristic algorithms, which are

supposed to produce approximately best solutions, are known not

to solve spatial problems adequately. Consequently, the preferred

alternative is to use metaheuristic algorithms. (This terminology

and the relevant issues will be explained in detail in the Materials

and Methods section). In the past, simulated annealing has often

been used for this purpose, especially as incorporated in the

Marxan software package [14]. However, it has been found to be

relatively slow [15], and Marxan only permits the use of a pre-

specified set of criteria (size, shape [compactness], and a

generalized cost) [16]. This analysis uses a tabu search algorithm

[17] and a new (soon to be released) version of the ConsNet

software package [18,19]. Tabu search is known to be a fast

metaheuristic algorithm for a wide variety of optimization

problems [17]. Besides implementing tabu search, ConsNet allows

the incorporation of an indefinite number of criteria into the

identification of priority sets using a modification of the Analytic

Hierarchy Process (AHP) [20], which ensures that the multi-

criteria analysis is consistent with multi-attribute value theory

(MAVT) [21,22]. ConsNet has inbuilt algorithms to incorporate

compactness and connectivity. Other criteria can be modeled

using input from the user.

The group Opuntia (prickly pear or nopal) consists of two genera,

Opuntia and Nopalea, of the Cactaceae family. The group

evolutionarily originated in the American continent, and species

from these genera can be found from just south of the Arctic circle

in Canada to the tip of Patagonia in South America [23], and from

sea level to an altitude of 5 100 m in Peru [24], in climates with no

more than 500 cm of annual precipitation [23]. The country is the

world’s most important center of diversity of genera and species of

cacti, including Opuntia, most of which are endemic to it (73% and

78%, respectively, for genera and species [25]). There exist about

200 recognized species, of which at least 84 are found in Mexico

(and, depending on taxonomic choices, these numbers may be

higher) [26]. Mexico thus has one of the world’s highest Opuntia

species richness [27], so conservation of this genera is important

for both biodiversity persistence and economic sustainability. Most

of these species occur in arid or semiarid regions, where they are

subject to different types of threat generally due to human

activities, primarily habitat conversion, but also unsustainable

harvesting for direct use and for sale in national and international

markets [25,28]. These sales are economically important because

these cacti are often ideal crops for arid regimes [23]. However,

because of the threats, most genera are legally recognized as being

in need of a certain level of protection.

Two factors mitigate against designating strictly protected areas

for Opuntia conservation in Mexico. First, there is extensive

endemism, including micro endemism (see Table 1), but the

endemics are widely dispersed over the arid regions of the country.

Consequently, conservation cannot be focused on a small set of

specific areas to be legally designated as strictly protected and

removed from routine human use. Second, in their native habitat,

Opuntia species have extensive human use: to feed cattle, goats,

sheep, and horses, and to prepare food and other derived products

for human consumption while they are also a food source for a

variety of wild fauna [25,29]. Such use has resulted in two

developments that have conservation implications: (i) an increase

in hybridization between species that were brought under

domestication from wild populations; and (ii) a decrease in

morphological diversity within isolated domesticated populations

which may eventually lead to a decrease in genetic variation [30].

The first development leads to the problematic situation that

Opuntia taxonomy remains in flux; consequently, conservation

goals should include large areas for management so that all taxa of

potential value are likely to be represented (which may not happen

Tabu Search for Conservation of Opuntia in Mexico


if there is a focus on a small ‘‘optimal’’ set of areas). The second

development also entails the same recommendation but for the

goal of maintaining as much genetic diversity as possible.

Where they occur, Opuntia species are locally abundant and

often form dominant components of natural floras, especially in

arid regions, where they have substantial environmental

importance. They are a major ecological component of the

floras of the Chihuahuan and Sonoran Deserts (where they form

assemblages also known as nopaleras). They contribute signif-

icantly to soil stability and constitute an important dietary

component of a variety of mammal species including white-

tailed and mule deer (Odoicoileus virginianus and O. hemionus),

rodents (Peromyscus, Dipodomys, and Neotoma spp.), and coyotes

(Canis latrans) [31,32]. They also provide nesting sites and food

for a variety of insects, birds, rodents, and lagomorphs [30]. In

spite of their economic and environmental importance, Opuntia

species remain relatively little studied [24], and a systematic

conservation plan for them has not previously been formulated

for Mexico (or elsewhere).

The purpose of this study is to develop such a systematic plan by

prioritizing areas for conservation attention. We addressed the

hypotheses that an adequate Opuntia conservation in Mexico (i)

require a much larger area than could reasonably be put under

protection without routine human presence and use; (ii) require

incorporation of a wide variety of criteria partly to make

management feasible; and (iii) require innovative computational

algorithms to find satisfactory solutions that have a significant

potential for implementation on the ground. The methodology

developed here was specifically applied to Mexico but can be

transported with no modification to other areas which are centers

of Opuntia diversity. Moreover, it is equally applicable to all widely-

dispersed taxa. First, a standard maximum entropy algorithm

[33,34] was used to create species distribution models for 60

Opuntia species based on occurrence data and environmental

variables. Second, targets of representation were assigned to

Opuntia species which were inversely proportional to their

estimated ranges in order to prioritize endemic and other rare

species. Third, the area prioritization problem was reformulated as

a constrained optimization problem. There were two hard

constraints: the satisfaction of the biodiversity representation

targets just mentioned, and the inclusion of all existing formally

protected areas as priority areas. The latter constraint incorpo-

rated the spatial criterion of alignment to the extent required by

this problem. The other spatial criteria, which are related to

management options, were incorporated into an objective function

to be minimized with weights on the area, connectivity, and shape

of priority areas. Minimization was achieved using a modular

adaptive tabu search algorithm [35]. Three different objective

functions were used and each resulted in a map of the distribution

of priority areas for Opuntia conservation in Mexico. These three

plans are thus available to policy-makers to be ranked on the basis

of socio-economic and other criteria. Beyond the identification of

sets of priority areas, the analysis here does not aim to devise

management plans because these will depend on detailed analyses

of local contextual preferences after a final set of priority areas

have been selected.

Results and Discussion

Species’ Distribution Models and TargetsFigure 1 shows the occurrence records for Opuntia in Mexico

and the existing protected areas. Models for 60 species satisfied the

adequacy criteria used for this analysis (Table 1), that is, they were

deemed accurate enough to be used to prioritize areas for

conservation management. Figure 2 shows the predicted distribu-

tion for O. chaffeyi, which had the fewest occurrence records (four

data points). This species exhibits an extreme form of micro

endemism, which was quite common for this dataset (see Figure 3).

Models for three species had AUC values ,0.8 and were rejected:

O. littoralis, O. phaeacantha, and O. violacea; these had 10, 66, and

21 records, respectively.

Figure 3 shows the distribution of the number of species versus

their percentage targets of representation. Because there were

many species with a low total representation (Table 1), that is the

number of cells in which they are expected to occur, a large

number of the species have very high percentage targets. Even

though, at least for microendemics, this high percentage need not

translate into large areas, this result is consistent with the

presumed difficulty of attempts at Opuntia conservation through

the creation of strictly protected areas.

Conservation Area NetworksThere were 39 475 cells designated as protected areas at the

resolution of this analysis. This means that about 9% of the total

area of Mexico is formally protected. Given that, globally, setting

aside 10% or 12% of the area of each country for biodiversity

protection is usually regarded as a sufficiently ambitious goal [10],

it would be socio-politically difficult to designate more areas for

strict protection for Opuntia conservation.

If no spatial criteria were used (the ‘‘null’’ solution in the

discussion below), all targets of representation for all species can be

achieved in 133 570 new cells, that is, cells outside the existing

protected areas. Such a solution has 10 221 clusters (or connected

components). When spatial criteria were used, three separate

nominal conservation plans were formulated. Plan A incorporated

the minimization of area and maximization of compactness with

equal weights. Plan B gave a three-fold preference to the former.

Plan C included these criteria with equal weights but also

incorporated achieving connectivity with a relative weight of

one-half compared to the other two criteria. For each plan, two

different solutions (labeled‘‘1’’ and ‘‘2’’) were obtained using

different starting points for the search. Figure 4 shows the solution

or conservation area network selected under Plan A with the least

area; Figure 5 is the corresponding map for Plan B. Figure 6 is the

map with highest connectivity for Plan C. Table 2 gives the

number of cells, shape value (the perimeter–to–area ratio), and the

number of clusters. Finally, all plans require about one-third of

Mexico’s total area to be put under conservation. Table 3 shows

the extent to which the major vegetation types of Mexico were

included in the different plans. It did not come as a surprise that

the dominant vegetation type, under all plans, was xeric scrubland

since these are assemblages typically dominated by Opuntia species.

More pertinent to this study was the result that the next most

common vegetation type consisted of agricultural and forestry

lands. Since these are subject to intensive human use, their

prevalence underscores the point being emphasized here, that

Opuntia conservation areas should not be conceptualized as regions

of strict human exclosure. Rather, both strictly protected areas for

the conservation of microendemics, and management programs

admitting human use for widely distributed species should be

devised and should focus only on the long-term persistence of

Opuntia species. For example, Figure 7 shows the agricultural and

forestry lands incorporated into Plan C1. All plans included

substantial areas of oak, pine, and deciduous forests, which were

not intuitively expected until the performance of this analysis.

Even at a fine resolution, what was striking was the extent of

spatial similarities between the plans. All plans select a large

number of areas in central and south-central Mexico, including



Table 1. Opuntia Species in Mexico.

Species No. of Records Status AUC Total Representation Target (%)

O. albicarpa 15 E 0.97 9820.17 76.44

O. amarilla 6 E 0.99 2957.95 93.22

O. andersonii 11 ME 1 793.83 98.64

O. atrispina 4 E 1 912.38 98.32

O. atropes 155 E 0.97 8389.94 80.31

O. azurea 12 ME 0.94 16487.34 60.45

O. basilaris 1 E 0

O. bensonii 18 E 0.99 11563.69 72.03

O. bravoana 3 ME 0

O. chaffeyi 4 ME 1 176.35 100

O. chavena 81 E 0.99 8497.89 79.94

O. chlorotica 17 ME 0.97 33807.62 15.19

O. cochinera 41 E 0.98 3045.79 92.94

O. cretochaeta 8 E 0.94 34174.75 10

O. decumbens 65 NE 0.92 10869.89 10

O. depressa 46 E 0.98 5183.09 88.54

O. durangensis 46 E 0.99 8115.1 80.64

O. elizondoana 6 ME 1 3922.38 91.04

O. engelmannii 541 E 0.94 11484.34 73.64

O. erinacea 2 E 0

O. excelsa 47 E 0.99 3060.88 93.51

O. feroacantha 9 ME 0.97 5595.17 86.02

O. fragilis 1 ME 0

O. fuliginosa 206 E 0.95 10672.4 74.61

O. grahamii 1 ME 0

O. guilanchi 43 E 0.96 15867.8 60.05

O. heliabravoana 39 E 0.98 1432.24 97.24

O. howeyi 2 ME 0

O. huajuapensis 25 E 0.99 3621.17 92.11

O. humifusa 1 ME 0

O. hyptiacantha 144 E 0.97 7069.52 82.85

O. icterica 220 E 0.96 9404.29 76.82

O. incarnadilla 12 E 1 3695.09 91.31

O. joconostle 104 E 0.97 7516.44 82.24

O. lasiacantha 158 E 0.95 9717.48 76.15

O. leucotricha 132 E 0.97 6919.58 83.67

O. littoralis 10 E 0.6 14805.21 0

O. macrocentra 7 ME 0.96 10434.75 74.06

O. macrorhiza 9 E 0.95 18508.28 55.65

O. matudae 30 E 0.99 3092.02 92.98

O. megacantha 72 E 0.96 8038.74 79.24

O. megarhiza 16 E 1 3563.6 91.42

O. microdasys 163 E 0.94 9665.43 77.96

O. nejapensis 2 E 0

O. neochrysacantha 1 ME 0

O. nigrita 13 E 0.9 25834.49 32.5

O. oligacantha 24 E 0.97 7617.36 82

O. olmeca 1 ME 0

O. orbiculata 38 E 0

O. oricola 2 ME 0



the densely populated Transvolcanic Belt. Areas in the Chihua-

huan desert just south of southwest Texas also have high priority.

By and large, the priority areas identified here coincide with those

identified as high to moderate priority obtained from a multi-taxa

gap analysis of priority areas for biodiversity conservation that

included a diverse array of faunistic (all vertebrates, several buttery

and insect genera) and oristic groups (several genera of owering

plants, but not Opuntia) in Mexico [36]. That gap analysis

identified as high, very high, and extremely high priority areas

large regions of the northwest (including the states of Sonora and

Chihuahua), the Transvolcanic Belt, and the southwest (including

the states of Guerrero and Oaxaca). Previous regional studies of

cacti, including Opuntia species, identified the southern portion of

the Chihuahuan desert as a priority area; those results are

consistent with the areas selected in this analysis [37,38]. In this

region, the selected Opuntia priority areas of this analysis widely

overlapped with the earlier Mexican gap analysis [36]. However,

there were also large regions that this Opuntia study identified as

being of high priority but the earlier Mexican gap analyses

identified as having low or very low priority. This was the case for

the southern portion of the Baja peninsula (including the states of

Baja California Sur and the southern part of Baja California).

Thus this analysis extends those earlier results, which did not

include Opuntia species. Finally, regions identified as moderate to

high priority in the earlier gap analysis coincided with the priority

areas identified here in the northern portion of the Baja peninsula

Table 1. Cont.

Species No. of Records Status AUC Total Representation Target (%)

O. pachona 11 E 0.96 10811.65 72.59

O. pachyrhiza 7 E 0.99 9949.49 76.7

O. parviclada 102 ME 0.98 14158.64 66.46

O. phaeacantha 66 E 0.82 28255.9 0

O. pilifera 1 E 3288.14 92.62

O. polyacantha 2 ME 0

O. pottsii 166 ME 0

O. puberula 79 NE 0.97 8844.52 10

O. pubescens 49 E 0.95 12250.87 70.68

O. pumila 4 E 0.97 6144.97 86.51

O. pycnacantha 2 E 0

O. pyriformis 1 E 0

O. reflexispina 11 E 0

O. rileyi 265 E 0.96 21695.89 49.48

O. ritteri 1 ME 0

O. robusta 28 E 0.94 9718.18 76.72

O. rzendowskii 7 E 1 1343.62 97.37

O. scheeri 2 ME 0.22 2218.24 0

O. schotti 2 E 0

O. setispina 12 ME 0

O. spinulifera 11 E 0.95 8732.19 78.05

O. spraguei 247 E 0.96 26206.42 38.59

O. stenopetala 218 E 0.98 4791.66 88.43

O. streptacantha 115 E 0.97 8009.59 81.31

O. stricta 7 NE 0.94 18941.48 10

O. tapona 5 E 0.96 7270.1 82.12

O. tehuacana 204 ME 1 30053.72 25.37

O. tomentosa 16 E 0.97 8091.83 80.84

O. undulata 81 E 0.92 32890.73 14.02

O. velutina 4 E 0.96 7921.01 81.29

O. vilis 68 ME 0.98 7039.74 83.72

O. violacea 21 E 0.73 41333.63 0

O. wilcoxii 16 E 0.84 19920.63 53.65

O. zamudioi 11 E 0.99 21133.86 48.44

All 84 Opuntia species from Mexico are included. AUC values have been rounded off to two decimal places. The absence of an AUC value indicates that no speciesdistribution model was constructed. The absence of a target indicates that the model did not satisfy the adequacy criteria for use in the prioritization exercise. Thetargets are percentages of the total expected value for the species in the study area. With respect to status: E = endemic; ME = microendemic (rare); NE = non–endemic.doi:10.1371/journal.pone.0036650.t001



(including the northern part state of Baja California). Areas in the

Chihuahuan desert just south of southwest Texas also have high

priority.

Tradeoffs in Conservation Area NetworksTable 2 also provides the tradeoffs involved in attempting to

optimize shape and connectivity. Measured by the perimeter-to-

area ratio, the null solution is four times worse than the one with

the best shape (Plan C1). As Plans A and B show, optimizing for

shape automatically led to optimization for connectivity. However,

best connectivity was achieved when it was explicitly included as a

criterion in the multi-criteria analysis (Plan C1). Over all, Plan C1

performs best because it achieves both the highest shape and

connectivity performance, and only at a cost of 15% more in the

number of cells prioritized. Given that the nominal priority areas

are intended to be managed for continued human use, but with a

focus on the protection of Opuntia species, this 15% cost is almost

certainly not too exorbitant a price to pay to achieve the spatial

coherence provided by Plan C1.

The selected priority areas for Opuntia species show how

connectivity can be best achieved between the priority areas.

Since biosphere reserves were included in the analysis, some

selected areas can easily be connected by them. For example, in

the northern part of the country, the Desierto del Vizcano and

Valle de los Cirios are large biosphere reserves located in the

middle of the Baja peninsula. These reserves can serve to connect

the Opuntia priority areas selected in the northern portion in the

state of Baja California, with those from the southern portion,

including the state of Baja California Sur. Opuntia priority areas

located in the northwest in the states of Sonora and Sinaloa can be

connected by the large remnant fragments of natural habitat still

available in the region. In central Mexico, the Opuntia priority

areas can be connected using the results of a previous connectivity

analysis which incorporated the representation of endemic

mammals [39]. The priority areas established in that study can

be used to connect the Opuntia priority areas located in the

Mexican plateau, the Transvolcanic Belt, and Oaxaca. However,

some Opuntia priority areas present a more difficult challenge to

achieving connectivity and organization into large prioritized

blocks. For example, the isolated Opuntia priority areas located in

the north, south, and Pacific lowlands will require a different

approach. In these cases, there must be further tradeoffs between

the total size of the areas prioritized for conservation and

connectivity.

Final ReectionsThe results of this analysis confirm the hypotheses: (i) adequate

Opuntia conservation in Mexico would require a much larger area

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Figure 1. Opuntia Records in Mexico. The existing protected areas are shown in gray. The red dots show the sites from which Opuntia occurrencerecords were available. The states that are named are those that are mentioned later in the Discussion.doi:10.1371/journal.pone.0036650.g001



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Figure 2. The predicted distribution of Opuntia chaffeyi in Mexico. This distribution model was created using only four records and,accordingly, shows a highly restricted range. Darker areas have higher predicted habitat suitability.doi:10.1371/journal.pone.0036650.g002

Figure 3. Distribution of representation targets. A large number of species have high percentage targets indicating highly restricted ranges.doi:10.1371/journal.pone.0036650.g003



than could reasonably be put under protection without routine

human presence and use; (ii) it would require incorporation of a

wide variety of criteria partly to make management feasible; and

(iii) innovative algorithms computational methods would be

needed to find satisfactory solutions that have a significant

potential for implementation on the ground. It should be

emphasized that, although the purpose of this paper was to

identify areas where Opuntia species can be found under human

use, these are also the areas in which microendemics are present

and should deserve special attention in future conservation

programs.

As Table 2 shows, achieving spatial coherence in shape and

connectivity to facilitate dispersal necessary for range expansion

and maintenance of genetic diversity came at a price: more area

had to be prioritized. Optimizing shape (Plan A), and giving it the

same weight as minimizing the area, required 15% more area than

meeting all representation targets without concern for shape. If

shape was given a relative weight of only one-third relative to the

area (Plan B), the additional area required was only 6%. There

was a roughly linear dependence between the relative importance

of shape and the additional cost in terms of increased area.

However, enhanced connectivity could be achieved without

additional cost compared to Plan A, also requiring 15% more

area beyond the null model (Plan C). This means that, for this data

set, while optimizing both shape and connectivity was individually

expensive, there was enough correlation between these two

parameters to make their joint optimization no more expensive.

Management for conservation and restoration appears to have

been successful in many Mexican biosphere reserves, in which

human activities include sustainable production and exploitation

of natural resources. As a consequence, biosphere reserves have

been more effective in preventing land use and land cover change

compared to other formally (decreed) protected and non-protected

areas [40,41]. The results presented here suggest that successful

conservation programs should expand even beyond biosphere

reserves and include other priority areas into expanded conser-

vation area networks. As this analysis shows, such networks can be

particular important for the conservation of widely–dispersed taxa

as Opuntia which overlap with routine human presence and use.

Moreover, in a result that has the same implications as this

analysis, the multi-taxa Mexican gap analysis identified a

significant proportion of priority areas for biodiversity conserva-

tion outside the formally (decreed) protected areas [36]. Thus,

conservation area networks with sound management for conser-

vation and restoration in extended blocks of multiple–use priority

areas provides a more promising alternative for Mexico than

traditional formally protected areas which exclude or allow little

human presence and use of resources.

It should be noted that the database used for this project is being

continually updated and, during the time while this study was

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Figure 4. Plan A. The existing protected areas are shown in black. The additional selected areas are in gray.doi:10.1371/journal.pone.0036650.g004



being conducted, nine species of Opuntia that are new to Mexico

have been discovered and their occurrence points have been

added to the database. These species were not included in the

analysis because they had too few occurrence points for species

distribution models to be constructed–their inclusion would not

have affected the results of this analysis. Once there are enough

occurrence records for these species, the results here should be

updated. There is an ongoing effort in that direction.

Turning to computational issues, before the development of the

tabu search methods described in this paper, to the best of our

knowledge, tabu search had only once been previously applied to

problem of identifying conservation area networks [42] but the

examples that were solved, besides being small in size, only

involved the accomplishment of biodiversity representation targets

and no spatial analysis. They were also not intended as practical

policy recommendations. Thus the full power of tabu search to

solve complex optimization problems was not exploited. The

results reported here suggest that tabu search is one of the most

promising methods for solving the hard spatial optimization

problems that arise during biodiversity conservation planning. The

methods discussed here in detail for the first time were used, along

with an earlier version of the ConsNet software package, by

Conservation International to select priority areas in the Papua

province of Indonesian New Guinea [42], in a recent study of

Mexican herpetological biodiversity [43], and is being currently

being used to prioritize areas in Colombia (M. C. Londono,

personal communication). However, in only the first of these

instances (which remains unpublished) was an extensive spatial

optimization attempted.

Materials and Methods

Study Region and Species DataFor this analysis, Mexico was divided into 431 913 cells with an

average area of 4.64 km2 (SD = 0.0041 km2) at a 0.02u60.02ulongitude 6 latitude resolution. All species’ data and environmen-

tal layers used to model distributions (see below) were georefer-

enced or resampled to this resolution. Information on the

protected areas of Mexico was obtained from the Mexican

National Commission on Protected Areas (www.conanp.gob.mx/

sig; last accessed 27 July 2010).

Species’ occurrence data, which were necessary to construct the

species distribution models, were available for 84 species from a

comprehensive set of biological collections (see Acknowledgments).

There were 1–541 records available for each species (with an

average of 66 records, SD = 92.08; total number of records = 4

456). However, sufficient data to attempt model construction were

available only for 63 of the species listed in Table 1. Of these, 23

were microendemic, 58 were endemic to Mexico, and three were

considered Mega-Mexico species (those with a distribution spread

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Figure 5. Plan B. The existing protected areas are shown in black. The additional selected areas are in gray.doi:10.1371/journal.pone.0036650.g005



across Mexico and the arid parts of the United States, that is,

Mega-Mexico 1 [Opuntia stricta] or those with a distribution spread

across Mexico and south up to northern Nicaragua, that is, Mega-

Mexico 2 [O. puberula and O. decumbes]; [44]). Two (O. bravoana and

O. excelsa) were included as at–risk species by the Norma Oficial

Mexicana 059–ECOL–2001 (NOM), a technical standard issued

by the Mexican federal government that specifies the conservation

status of species [45].

Models of Species’ DistributionsThe species distribution models were constructed from species’

occurrence points and environmental layers using a maximum

entropy algorithm. The Maxent software package (Version 3.3.4;

[34]) was used to construct the models. Maxent has been shown to

be robust for modeling species distributions from occurrence

(presence–only) records for a large number of taxa [46]. Following

published recommendations [34,47,48], Maxent was run without

the threshold and hinge features and without duplicates so that

there was at most one sample per pixel; linear, quadratic, and

product features were used. The convergence threshold was set to

a conservative 1.061025. For the AUC, that is, the area under the

receiver operating characteristic (ROC) curve [34], averages over

100 replicate models were computed. For each model the

test:training ratio was set to 40:60 following Phillips and Dudık

[34] which means that models were constructed using 60% of the

data and tested with the remaining 40%. No attempt was made to

model species with fewer than four records because such models

are typically unreliable. Consequently, models could be construct-

ed for 63 species.

Constructing species distribution with ,10 records is always

open to question. Typically $20 records are recommended

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Figure 6. Plan C. The existing protected areas are shown in black. The additional selected areas are in gray.doi:10.1371/journal.pone.0036650.g006

Table 2. Spatial properties of Plans.

Plan No. of Perimeter–area No. of

New Cells Ratio Clusters

A1 153 478 0.098 598

A2 153 694 0.098 659

B1 140 081 0.207 2 317

B2 140 636 0.205 2 089

C1 153 941 0.097 265

C2 152 461 0.11 316

Null 133 570 0.416 10 221

A, B, and C refers to the three plans; 1 refers to the first solution; 2 to thesecond. The Null plan is the one in which no spatial criteria are used.doi:10.1371/journal.pone.0036650.t002



Table 3. Vegetational analysis of plans.

Vegetation Type Null A1 A2 B1 B2 C1 C2

Xeric Scrubland 201557 229 351 231 244 205 868 208 568 224 186 229 940

Agricultural–Forestry Lands 158660 178 371 173 712 176 023 176 236 186 449 179 503

Oak Forest 50209 57 207 64 649 52 311 53 685 56 116 60 190

Coniferous Forest 49207 67 860 66 088 53 560 52 715 68 565 63 401

Deciduous Forest 44177 51 606 50 344 45 662 45 899 50 743 48 210

Grassland 31663 39 626 36 967 30 411 31 023 39 333 36 818

Rainforest 14890 15 382 15 066 15 335 14 222 15 460 14 894

Aquatic Vegetation 13442 13 771 13 618 13 275 13 224 13 567 13 591

Sub-deciduous Forest 7224 8 208 8 853 8 180 8 055 8 083 8 301

Cloud Forest 5628 6 106 6 222 6 612 5 345 6 756 6 812

Thorn Forest 3912 3 591 3 591 3 842 3 925 3 666 3 675

Only the most important types of land cover are shown. A, B, and C refers to the three plans; 1 refers to the first solution; 2 to the second. The Null plan is the one inwhich no spatial criteria are used. The areas are in sq km.doi:10.1371/journal.pone.0036650.t003

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Figure 7. Agricultural and forestry areas in the new prioritized cells under Plan C1. These are shown in red when they intersect with thenew prioritized areas (that is, other than those in the existing protected areas). The solution corresponds to that in Figure 6.doi:10.1371/journal.pone.0036650.g007



though, according to a recent study [49], Maxent model

performance stabilizes at 10 records and even five records are

sometimes regarded as sufficient [50]. However, restricting

attention to species with $10 records would have removed 32 of

the 84 species, rather than 21, among them seven more

microendemics (see Table 1) of obvious conservation significance.

Consequently, it was decided to model these species but to subject

the results to expert scrutiny besides using the tests described

below. All these models survived such scrutiny.

Two tests were used to assess model performance: (i) A relatively

conservative threshold of 0.8 was used for the AUC [49,50,51].

(An optimal model would have an AUC close to 1 while a model

that predicted species occurrences at random would have an AUC

of 0.5. Only one species [O. wilcoxii] had an AUC value between

0.8 and 0.9.); (ii) For eight internal training and test binomial tests

performed by Maxent (two each for minimum presence, 10

percentile presence, equal sensitivity and specificity, maximum

sensitivity plus specificity), a p-value ,0.05 was required. In

general the results indicated that though there were few data

points from the very north of Mexico, there was no reason to

believe that there was a substantial bias against those regions in

model results.

The environmental layers used are listed in Table 4. These

include four topographical variables (elevation, slope, aspect, and

compound topographical index) and 19 bioclimatic variables. The

latter were obtained from the WorldClim database (www.

worldclim.org; last accessed 28 February 2010;[52]). Elevation

data were obtained from the United States Geological Survey’s

Hydro–1K DEM dataset (http://eros.usgs.gov/#/Find_Data/

Products_and_Data_Available/Elevation_Products; last accessed

16 February 2012). Slope, aspect, and the compound topograph-

ical index were derived from the DEM using the Spatial Analyst

extension of ArcMap 9.3.

The output from these models directly quantifies habitat

suitability for a species by computing the relative probability of

its presence in each cell of the study area. These probabilities

establish the potential distribution of a species (and are sometimes

interpreted as providing an approximate ecological niche model

[53,54]). The predicted distribution is obtained using biological

information such as dispersal behavior and other constraints

including vicariance factors that limit the potential distribution. In

this analysis, the refinement process used the Uso del Suelo y

Vegetacion (USV) map [55], a recent digital vegetation map of

Mexico which distinguishes between primary and secondary

vegetation. Cells transformed into agrosystems and rural or urban

settlements were assumed not to be suitable habitats for endemic

and at–risk species and were excluded from the potential

distributions. Model output was interpreted as probabilistic

expectations for each species in a cell [10,12]. Under this

interpretation, the sum of these expected values across a set of

cells provides the expected occurrence value for the species, that is,

the expected number of cells in which the species would be found.

Targets of Representation, Area Constraints, and SpatialGoals

The goal of each Opuntia conservation plan was to provide

adequate representation of each species within a prioritized set of

cells with as little total area as possible, after including all existing

protected areas, while achieving spatial coherence through

compactness of shape and contiguity (connectivity) of prioritized

cells. Following what has become standard practice in systematic

conservation planning [1,2,5], adequate representation was

interpreted quantitatively as a specified number of prioritized

cells in which the species must be present.

In general, there is no fully satisfactory biological rationale for

choosing these quantitative targets of representation [2,55,56]. In

some circumstances, population viability analyses [57] may

provide guidance but such analyses typically require abundance

data over a large number of time steps [58]. Such data were not

available for a single Opuntia species in Mexico. Consequently,

targets were assigned to reect the rarity and endemicity status of

the species. First, an arbitrary relatively small but widely used

target of 10% of the expected occurrence within cells [12] was

assigned to the three non-endemic species (O. decumbens, O. puberula,

and O. stricta). Next, the same target was assigned to the most

abundant species (O. cretochaeta) with an expected total represen-

tation of 3 417 475 and a target of 100% was assigned to the least

abundant species (O. chaffeyi) with an expected total representation

of 17 635. For all other species, targets were assigned on a linear

scale between 10% and 100% in inverse proportion to their

expected representation in the study area. (Preliminary runs with

upper targets between 80% and 100% resulted in insignificant

improvements with spatial economy–less than 3% of the area

selected. Since there was no biological justification for any of these

values between 80% and 100% they were not used. However, it

was presumed that a target ,80% would not be sufficient for the

geographically rarest, typically microendemic species.)

Satisfaction of these representation targets was one of two hard

constraints on the optimization problem. The other was the

inclusion of all existing protected areas (which satisfied the spatial

goal of alignment to the extent required in this analysis). Since

these are legally protected, they provided a natural foundation

Table 4. Environmental parameters for species distributionmodels.

Parameters

Annual Mean Temperature

Mean Diurnal Range

Isothermality

Temperature Seasonality

Maximum Temperature of Warmest Month

Minimum Temperature of Coldest Month

Temperature Annual Range

Mean Temperature of the Wettest Quarter

Mean Temperature of the Driest Quarter

Mean Temperature of the Warmest Quarter

Mean Temperature of the Coldest Quarter Annual Precipitation

Precipitation of Wettest Month

Precipitation of Driest Month

Precipitation Seasonality

Precipitation of Wettest Quarter

Precipitation of Driest Quarter

Precipitation of Warmest Quarter

Precipitation of Coldest Quarter

Elevation

Slope

Aspect

Compound Topographic Index

Temperatures are in uC, precipitation in mm, slope in meters. All with a pixelsize of 0.01u (1 kilometer resolution).doi:10.1371/journal.pone.0036650.t004



from which a conservation plan could be devised. The problem

then becomes one of constrained optimization: given these hard

constraints (that cannot be violated), the problem is to find

solutions that minimize the total area falling under the rubric of a

conservation plan while maximizing the compactness of shape and

connectivity of the set of selected areas. This constrained

optimization problem was solved through the construction of a

multi–criteria objective function with tabu search being used to

find the best solution.

Multi-criteria AnalysisMethods of multi–criteria analysis have been systematically

developed by the decision theory community since the 1980s

[22,59–61] and have been applied to a wide variety of decision

problems in conservation biology [11,20,62–64]. Canonically

simple decisions involve a single agent (the decision–maker) and

a single criterion, for instance, the number of at–risk species

accommodated by a conservation plan. Two more complex

decision scenarios involve: (i) multiple agents (or stakeholders) and

a single criterion; or (ii) a single agent and multiple criteria, for

instance, biodiversity representation, shapes of priority areas, and

economic cost. There is a formal (mathematical) isomorphism

between these two problems because combining preferences of

multiple agents according to a single criterion into an objective

function is equivalent to combining the distinct preferences of a

single agent using multiple criteria. Nevertheless, there is an

important philosophical difference [5,65]: the case of a single

agent and multiple criteria only involves aggregation over a single

agent’s preferences for various objectives whereas, in the case of

multiple agents, the aggregation involves the preferences of

different agents which may well not be commensurable in many

circumstances.

Thus, whenever possible, it is advisable not to use formal

methods for incorporating multi-agent preferences but to try to

ensure that a single set of preferences emerges through deliber-

ation between agents. This was the strategy followed here. Thus

the multiple-agent, single-criterion and the even more complex

multi-agent–multi-criteria decision problems will be ignored even

though there are obviously a large number of stakeholders for

Opuntia conservation in Mexico. It will be presumed that the

stakeholders will act jointly to choose between various plans and

that any differences between them can be modeled using the

weights that are given to various criteria in a multi–criteria

analysis. Finally, the decision analysis here will not explicitly

incorporate uncertainties (except that about species’ distributions

which are implicitly incorporated through the use of probabilistic

expectations) because these cannot be quantified in the present

context and are thus best left for incorporation during the

formulation of a management plan after a set of areas have been

prioritized.

A wide variety of methods for multi-criteria analyses have been

proposed [10,11,61] which range from those that are extensions of

standard single-criterion decision and economic theories [60,66] to

those which are not consistent with it, for instance, the much-used

Analytic Hierarchy Process (AHP) [67]. In particular, the AHP

suffers from the problem of rank reversal [22]: the inclusion of a

new alternative in an analysis can change the relative ranks of

existing alternatives even though nothing about their performance

has changed. Thus, though this analysis used the simple and

transparent preference elicitation method of the AHP, it used a

different aggregation formula [21,22] to avoid rank reversal and

achieve a final ranking of alternatives that is consistent with

standard multi–attribute value theory (MAVT) [68]. This meth-

odology was previously used to prioritize areas in a multi–criteria

analysis for selecting conservation areas in northern Namibia [20]

and Indonesian New Guinea [43]; it has also been incorporated

into the MultCSync software package for decision support in

conservation planning [69].

As in the AHP, preference elicitation was done on a ratio scale

between 0 and 9 through binary comparisons. There were three

criteria: (i) area, with the number of cells included in the set of

prioritized areas as its measurable attribute; (ii) shape, with the

perimeter–to–area ratio as its measure; and (iii) connectivity, with

the number of clusters (contiguous groups of prioritized cells) as its

measure. Three plans were produced using different preferences

for these criteria. In Plan A, only the first two criteria were used

and both were given equal weight. Plan B also used only the first

two criteria but the ratio between the number of cells and the

shape parameter was assumed as 3:1. In Plan C, all three criteria

were used and the number of cells, the shape parameter, and the

number of clusters were given weights in the ratios 2:2:1.

OptimizationThe constrained optimization problem required the minimiza-

tion of an objective function constructed using the multi–criteria

methods just discussed. There were three such objective functions

resulting in Plans A, B, and C. Traditionally, the solution of such

problems has been approached using two types of algorithms:

exact and heuristic. Exact algorithms, by definition, are guaran-

teed to produce optimal solutions. However, even without the

spatial component, these area prioritization problems are NP–

hard [10]: they reduce to the well–studied set cover [70–72] and

minimal cover [73–75] problems that can be exactly solved using

branch-and-bound algorithms [12]. However, NP–hardness

means that large problems may become computationally intrac-

table though the frequency of such a scenario remains debated

[10,12,76]. Meanwhile, heuristic algorithms based on selecting

cells with rare species first or cells with highest ‘‘complementarity’’

values (a ‘‘greedy’’ algorithm which selects cells with the most

under–represented species first) have been shown to be at most

marginally sub-optimal while remaining computationally fast and

easy to implement [10,12,77–79]. Consequently, these heuristic

algorithms have been much more often used in practice than exact

algorithms [2].

Once spatial criteria are included, the situation changes

drastically. Existing heuristic algorithms do not produce near-

optimal solutions and exact algorithms, even when they exist,

become intractable for problems much smaller than the ones

solved here. As a result, a fairly recently developed class of

metaheuristic algorithms have emerged as a tool of choice for

spatial conservation planning. These are algorithms that repeat-

edly use a set of heuristic rules to explore the search space and

escape from local optima. While metaheuristic algorithms are not

guaranteed to produce optimal solutions, a large body of work

shows that they routinely achieve near–optimality [10].

As noted earlier (in the Introduction), the first metaheuristic

algorithm used for spatial conservation planning was simulated

annealing [14]. However, existing implementations remain slow

and only allow a limited number of criteria to be incorporated

even after significant recent improvements [16]. In order to

improve performance the ConsNet software package, based on

tabu search [17], was developed for spatial biodiversity conserva-

tion planning [18,19]. Besides alignment, shape, and connectivity,

which were the relevant criteria for this analysis, ConsNet has

inbuilt options to incorporate replication: the number of indepen-

dent contiguous sets of cells in which a species is represented. It

also allows the incorporation of an arbitrary number of user–

specified criteria. The objective function to be minimized is



created using the multi–criteria method described earlier. This

analysis used a new version of ConsNet, which will be publicly

released soon.

Tabu Search. Tabu search is an iterative protocol that uses

dynamic memory structures to navigate the search space [17]. In

particular, the search maintains a tabu memory, which is a set of

rules that prohibits the search from making certain moves. One

common tabu restriction is that the search is not allowed to make

moves that would undo a recent move. Each tabu restriction

remains in effect for a set number of iterations (the tabu tenure).

Adjusting the tabu tenure dynamically [80,81] can improve

performance and prevent the search from getting trapped in a

local optimum [18,19]. At each iteration (starting from a current

solution), the search evaluates a set of neighboring solutions (its

current neighborhood). In general, each neighbor is a simple

modification of the current solution, but more complex transfor-

mations may also be used. The search then chooses the best

neighboring solution which is not tabu, and this becomes the

current solution for the next iteration. After each iteration, the

memory structures are updated based on the results and outcome

of the previous step.

The tabu search in ConsNet has two new features to improve

search performance: rule based objectives (RBO) and dynamic

neighborhood selection (DNS) [19]. RBOs use binary comparison

operators (rather than traditional numeric scores) to rank solutions

and make decisions at each iteration in the search [18]. RBOs

enable the search to incorporate precise ordinal rankings and may

be more compatible with user preferences in some multi-criteria

analyses. DNS is a meta-strategy which manages multiple

neighborhoods and attempts to choose the best one for the next

iteration in the search. A well constructed strategy can be used to

moderate the intensification and diversification of the search, and

can allow smaller neighborhoods to be used more effectively,

reducing the number of evaluations required during exploration.

This analysis introduced a new DNS strategy that performs

‘‘aggressive’’ spatial reorganizations when the search was not

finding improving solutions. This strategy was created by

observing that certain sequences of spatial rearrangement neigh-

borhoods could be used to transform a solution rapidly while

preserving the spatial characteristics. After a certain number of

iterations without finding a new best solution, the aggressive DNS

strategy implemented one of four different escape modes. The

duration and intensity of the escape maneuvers depended on the

problem size, recent search progress, and the performance of the

current solution. For instance, the search could explore deleting

the smallest clusters and then expanding existing clusters. The

changes were temporarily locked in place by the tabu tenure, and

the search was forced to explore new configurations. While not all

of these changes led to improved solutions, the ability to climb out

of local optima led to better solutions over the long run.

Initialization Heuristics. A metaheuristic algorithm begins

with an incumbent solution that it tries to improve upon. This

analysis used six heuristic algorithms (built into ConsNet) to

generate potential starting solutions (see Table 5). In all cases the

cells corresponding to the existing protected areas were included.

These heuristic solutions did not incorporate multiple criteria or

optimize a formal objective; they were only a quick approximation

for solving the basic set cover problem. Thus, these solutions were

not very useful except that they serve as a starting point for a more

detailed metaheuristic search.

Metaheuristic Search. The optimization procedure for each

objective involved multiple steps. During the first step, the search

chose an initial solution and ran a prolonged search. This step

used the ‘‘aggressive’’ dynamic neighborhood strategy to help

improve the spatial characteristics of the solution. Next, it carried

out an intense refinement search starting from the best solution

discovered in the previous step. This search uses a neighborhood

which examined a large number of moves at each iteration to

make improvements that may have been missed otherwise. This

search ran slower, but was useful for refining high quality

solutions. Finally, this entire process was repeated from a different

initial solution as a starting point. A comparison of solutions

obtained from two different starting points can be used to gauge

how well the search was converging to a near optimal solution.

Objective A (Plan A) gave equal weight to two criteria:

minimization of the number of cells (0.5) and minimization the

shape (0.5)(lower values for shape indicate better compactness).

The sub-score for the number of cells was scaled linearly between

133 000 and 200 000 and the shape was scaled linearly

between0.01 and 0.45. These upper and lower bounds were

determined by examining the heuristic solutions. The initial search

started from the best available heuristic solution and ran for 46106

iterations. This number was chosen because it is about 10n, where

n is the number of cells. The solution was called A1. Next, anew

search was run using the same protocol but starting from the worst

heuristic solution; the resulting solution was called A2. (These

solutions/plans will also be referred to as Plans A1 and A2; and

similarly for Plans/Objectives B and C.)

Objective B (Plan B) considered the same criteria as A but used

different weights: minimize the number of cells (0.75) and improve

shape (0.25). The search steps followed the same procedure and

two more solutions were generated (B1 and B2).

Objective C (Plan C) considered three criteria: minimization of

the number of cells (0.4), minimization of the shape (0.4), and

minimization of the number of clusters (0.2). The sub-score for the

Table 5. Heuristic algorithms used to generate initialsolution.

Algorithm Rules

1 Select cell with species furthest from target.

Ties broken using richness.

Ties broken using lexical order.

2 The same as 1, but ties broken with adjacent cell

before lexical order use.

3 Select cells with rarest species.





5 Select cells with rarest species.


Repeat until a threshold is met for number of satisfied

targets.

Select cell with species furthest from target.


Repeat until a threshold is met for number of satisfied

targets.




doi:10.1371/journal.pone.0036650.t005



number of clusters was scaled linearly between 200 and 2000.

When the computation of clusters is enabled, the search ran

slower, particularly if the solution had poor spatial organization.

For large data sets with clustering, starting the search from a

solution that has coherent spatial organization can save time. For

that reason, initial starting point for these runs was the best

solution (scored with objective C) from the possible candidates A1,

A2, B1 and B2. The initial search ran for 26106 iterations (fewer

iterations could be used because the starting point was a high

quality solution). Next the refinement search was run for 50 000

iterations; the best solution was saved C1. Finally, we ran a new

search starting from the worst solution among the candidates A1,

A2, B1, and B2: the worst solution was chosen to test whether the

search was being confined to a local optimum. While there is no

guarantee that this protocol detects all such local optima, past

experience with tabu search indicates that almost all of them are

identified in almost all problems [18]. Repeating the process above

yielded one more solution C2.Computational Effort. The search was conducted on a Intel

Core i7 940 CPU with 4GB of RAM allocated to ConsNet. The

Java virtual machine was the Java Hotspot 64-Bit Server VM

(build 14.0-b16, mixed mode) and the operating system was

Windows Vista Ultimate Service Pack 1. Since multiple searches

were run concurrently, reported wall clock times are estimated

based on benchmarks. For Objectives A and B, 4126109solutions

were evaluated in 29.0 hours (3.956106 evals/s). For objective C,

2076109 alternatives were evaluated in 80.6 hours (688

000 evals/s).

Acknowledgments

Opuntia occurrence data were obtained from the following collections:

Centro Interdisciplinario de Investigacion para el Desarrollo Integral

Regional, Unidad Durango, IPN; Centro de Investigaciones Biologicas del

Noroeste, S. C.; Centro de Investigaciones Historicas y Sociales,

Universidad Autonoma de Campeche; Centro Regional del Bajıo; Colegio

de Postgraduados en Ciencias Agrıcolas, Campus San Luis Potosı; Colegio

de Postgraduados, Montecillo; Departamento de Botanica, Instituto de

Historia Natural de Chiapas; El Colegio de la Frontera Sur, Unidad San

Cristobal de las Casas; Facultad de Biologıa, Universidad Michoacana de

San Nicolas de Hidalgo; Facultad de Ciencias, Universidad Autonoma de

Baja California; Facultad de Ciencias, UNAM–Herbario–‘‘Marıa Agustina

Batalla’’; Herbario Alfredo Barrera Marin-Facultad de Medicina Veter-

inaria y Zootecnia, Universidad Autonoma de Yucatan; HerbarioDr. Jerzy

Rzedowski, Universidad Autonoma de Queretaro; Herbario ‘‘Eizi

Matuda’’ Universidad de Ciencias y Artes de Chiapas; Herbario ‘‘U

NAJIL TAKIN XIW’’, Centro de Investigacion Cientıfica deYucatan, A.

C.; Instituto de Biologıa, UNAM–Herbario Nacional de Mexico; Instituto

de Botanica, Universidad de Guadalajara; Instituto de Ecologıa, A. C.;

Instituto de Ecologıa A. C. Xalapa; Instituto de Investigaciones de Zonas

Deserticas, Universidad Autonoma de San Luis Potosı–Herbario ‘‘Isidro

Palacios’’; Instituto Nacional de Estadıstica, Geografıa e Informatica;

Instituto Nacional de Investigaciones Forestales, Agrıcolas y Pecuarias,

Campo Experimental Coyoacan, Coleccion Germoplasma; Instituto

Nacional de Investigaciones Forestales, Agrıcolas y Pecuarias, Campo

Experimental Coyoacan, Herbario Nacional Forestal ‘‘Biol. Luciano Vela

Galvez’’; Museo de Biodiversidad Maya, Universidad Autonoma de

Campeche; Universidad Autonoma Agraria Antonio Narro; Universidad

Autonoma Chapingo; Universidad Autonoma de Aguascalientes; Uni-

versidad Autonoma del Estado de Morelos; Universidad Autonoma de

Guadalajara; Universidad Autonoma de Nuevo Leon; Universidad

Autonoma de Tabasco; and Universidad Autonoma de Tamaulipas. We

thank all the curators and other personnel who provided access and help.

The database is available through the Unidad de Informatica para

Biodiversidad (Instituto de Biologıa, UNAM; www.ibiologia.unam.mx).

Author Contributions

Conceived and designed the experiments: SS MC PIR ML VSC LS.

Performed the experiments: MC ML. Analyzed the data: SS PIR.

Contributed reagents/materials/analysis tools: LS SS. Wrote the paper: SS

PIR VSC ML. Designed the software used in analysis: MC.

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